Instructions
Look at the color of the old coin. Copper coins tend to dull to a brown-black and they sometimes develop traces of verdigris -- green spots caused by oxidization. Old silver coins oxidize to a gray-black hue, and verdigris does not appear.
Give the coin a rub with your thumb. The oxidized layer on silver is very soft and should leave a grubby mark on your skin; the dirt on a copper coin is much more firmly fixed and won't come off in the same way.
Consider the size of the coins. As a general rule, old copper coins tend to be much bigger than old silver coins because the material they were made from was much cheaper.